From MAILER-DAEMON Fri May 18 09:14:52 2007 Date: 18 May 2007 09:14:52 -0300 From: Mail System Internal Data Subject: DON'T DELETE THIS MESSAGE -- FOLDER INTERNAL DATA Message-ID: <1179490492@mta.ca> X-IMAP: 1178037477 0000000026 Status: RO This text is part of the internal format of your mail folder, and is not a real message. It is created automatically by the mail system software. If deleted, important folder data will be lost, and it will be re-created with the data reset to initial values. From rrosebru@mta.ca Tue May 1 12:12:36 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 01 May 2007 12:12:36 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HityA-0003Au-KA for categories-list@mta.ca; Tue, 01 May 2007 12:08:46 -0300 Date: Tue, 1 May 2007 08:53:18 -0400 (EDT) From: Michael Barr To: Categories list Subject: categories: Tensor products (and C*-algebras) MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 1 I think it important to note that tensor products have no universal mapping property and no categorical definition. Given an internal hom, there might or might not be a tensor product that provides a left adjoint for it. Given a bifunctor, there might or might not be an internal hom (or two if the bifunctor is not symmetric) right adjoint to it. Another point is that the tensor product on abelian groups (or modules over any commutative right) has two universal mapping properties: It provides left adjoints for the quite obvious (but still not categorically defined) internal hom and also represents the functor that takes A to the functor of bilinear maps out of A x B. In any case, it makes no sense to ask what is the "right" tensor product. The right tensor product will be the one that is appropriate to the job you want to do with it. Michael From rrosebru@mta.ca Tue May 1 13:44:02 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 01 May 2007 13:44:02 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HivON-0003AG-ET for categories-list@mta.ca; Tue, 01 May 2007 13:39:55 -0300 Date: Tue, 1 May 2007 16:34:26 +0100 From: Miles Gould To: categories@mta.ca Subject: categories: Re: C*-algebras Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: RO X-Status: X-Keywords: X-UID: 3 On Sat, Apr 28, 2007 at 10:27:58PM +0200, Bas Spitters wrote: > It seems hard to find references to a categorical treatment of > C*-algebras. Concretely, there are several tensor products on > C*-algebras. Which one is `the right one' from a categorical perspective? Jeff Egger gave a talk on some of these ideas at the Nice PSSL - I'm somewhat surprised he hasn't replied to this thread. IIRC, the category of operator algebras is an involutive monoidal category with respect to one or other of the tensor products, and C*-algebras are exactly the involutive monoids w.r.t. this tensor product. Can't remember which one it was, though. Miles From rrosebru@mta.ca Wed May 2 10:09:01 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 02 May 2007 10:09:01 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HjEOx-0001RQ-LN for categories-list@mta.ca; Wed, 02 May 2007 09:57:47 -0300 Mime-Version: 1.0 (Apple Message framework v752.2) Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed Content-Transfer-Encoding: 7bit From: Marco Grandis Subject: categories: Preprint available: Collared cospans, cohomotopy and TQFT Date: Wed, 2 May 2007 11:47:48 +0200 To: categories@mta.ca Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: RO X-Status: X-Keywords: X-UID: 4 The following preprint is available: M. Grandis, Collared cospans, cohomotopy and TQFT (Cospans in Algebraic Topology, II) Dip. Mat. Univ. Genova, Preprint 555 (2007). http://www.dima.unige.it/~grandis/wCub2.pdf http://www.dima.unige.it/~grandis/wCub2.ps Abstract. Topological cospans and their concatenation, by pushout, appear in the theories of tangles, ribbons, cobordism, etc. Various algebraic invariants have been introduced for their study, which it would be interesting to link with the standard tools of Algebraic Topology, (co)homotopy and (co)homology functors. Here we introduce collared cospans between topological spaces, as a generalisation of the cospans which appear in the previous theories. Their interest lies in the fact that their concatenation is realised with homotopy pushouts. Therefore, cohomotopy functors induce 'functors' from collared cospans to spans of sets, providing - by linearisation - topological quantum field theories (TQFT) on manifolds and their cobordisms. Similarly, (co)homology and homotopy functors take collared cospans to relations of abelian groups or (co) spans of groups, yielding other 'algebraic' invariants. This is the second paper in a series devoted to the study of cospans in Algebraic Topology. It is practically independent from the first, which deals with higher cubical cospans in abstract categories. The third article will proceed from both, studying cubical topological cospans and their collared version. ____________ Marco Grandis From rrosebru@mta.ca Wed May 2 14:20:37 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 02 May 2007 14:20:37 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HjIQw-0007Nz-Cc for categories-list@mta.ca; Wed, 02 May 2007 14:16:06 -0300 Date: Wed, 2 May 2007 13:03:55 -0400 (EDT) From: Jeff Egger Subject: categories: Re: C*-algebras To: categories@mta.ca MIME-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 5 --- Miles Gould wrote: > Jeff Egger gave a talk on some of these ideas at the Nice PSSL - I'm > somewhat surprised he hasn't replied to this thread. I'm usually too shy to post to the mailing list, so I wrote Bas Spitters a personal reply instead. In this case, though, I have to set the record straight... > IIRC, the category > of operator algebras is an involutive monoidal category with respect to > one or other of the tensor products, and C*-algebras are exactly the > involutive monoids w.r.t. this tensor product. Can't remember which one > it was, though. The category of operator _spaces_ admits a (non-trivial) involutive monoidal structure---by which I mean a (non-commutative) monoidal structure together with a _covariant_ involution that reverses the order of tensoring. [Regarding a monoidal category as a one-object bicategory B, this means that the involution relates B with B^{op} rather than with B^{co}.] The tensor product is called the _Haagerup_ tensor product, and the involution I considered is the so-called _opposite_ operator space structure applied to the conjugate vector space. I had conjectured that involutive monoids in this involutive monoidal category (which, for the purposes of this mail, I shall call involutive operator algebras) are the same as C*-algebras, but eventually I discovered a counter-example which showed that involutive operator algebras are strictly more general than C*-algebras. (This was the direction which had less concerned me!) I apologise to anyone to whom I failed to mention this counter-example. Cheers, Jeff. Ask a question on any topic and get answers from real people. Go to Yahoo! Answers and share what you know at http://ca.answers.yahoo.com From rrosebru@mta.ca Wed May 2 14:20:37 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 02 May 2007 14:20:37 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HjIRJ-0007PY-Tr for categories-list@mta.ca; Wed, 02 May 2007 14:16:29 -0300 Date: Wed, 2 May 2007 10:09:42 -0700 From: Ashish Tiwari To: tiwari@csl.sri.com Subject: categories: ADDCT'07: LAST CFP: Abstract Submission Deadline May 4 Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 6 LAST CALL FOR PAPERS Automated Deduction: Decidability, Complexity, Tractability (ADDCT'07) Workshop affiliated with CADE-21 Bremen, Germany, 15 July, 2007 For complete information- http://www.mpi-inf.mpg.de/~sofronie/addct07.html Important Dates --------------- 4 May 2007: Abstract submission 9 May 2007: Paper submission 5 June 2007: Notification 15 July 2007: Workshop Topics of interest for ADDCT include (but are not restricted to): ----------------------------------------------------------------- - Decidability: - decision procedures based on logical calculi such as: resolution, rewriting, tableaux, sequent calculi, or natural deduction - decidability in combinations of logical theories - Complexity: - complexity analysis for fragments of first- (or higher) order logic - complexity analysis for combinations of logical theories (including parameterized complexity results) - Tractability (in logic, automated reasoning, algebra, ...) - Application domains for which complexity issues are essential (verification, security, databases, ontologies, ...) Submissions are encouraged in one of the following categories: -------------------------------------------------------------- - Original research papers (up to 15 pages, LNCS style, including bibliogra= phy); - Work in progress (up to 6 pages, LNCS style, without bibliography). - Presentation-only papers Submission of papers is via EasyChair at http://www.easychair.org/ADDCT2007= / Organizers and Chairs --------------------- Silvio Ghilardi (U. Milano) Ulrike Sattler (U. Manchester) Viorica Sofronie-Stokkermans (MPI,Saarbr=FCcken) Ashish Tiwari (Menlo Park) Program Committee ----------------- Matthias Baaz (T.U.Wien) Maria Paola Bonacina (U. Verona) Christian Ferm=FCller (T.U.Wien) Silvio Ghilardi (U. Milano) Reiner Haehnle (Chalmers U.) Felix Klaedtke (ETH Zurich) Sava Krstic (Intel Corporation) Viktor Kuncak (EPFL Lausanne) Carsten Lutz (TU Dresden) Christopher Lynch,(Clarkson U.) Silvio Ranise (LORIA/INRIA-Lorraine) Ulrike Sattler (U. Manchester) Renate Schmidt (U. Manchester) Viorica Sofronie-Stokkermans (MPI,Saarbr=FCcken) Ashish Tiwari (SRI) Luca Vigano (U. Verona) Contact For further informations please send an e-mail to Viorica Sofronie-Stokkermans sofronie@mpi-inf.mpg.de From rrosebru@mta.ca Fri May 4 15:30:29 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 04 May 2007 15:30:29 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1Hk2O2-0004W8-Am for categories-list@mta.ca; Fri, 04 May 2007 15:20:10 -0300 Date: Wed, 2 May 2007 10:55:07 -0700 From: John Baez To: categories Subject: categories: Beck-Chevalley for presheaves on groupoids? Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Disposition: inline Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 7 Hi - One of you must know the answer to this! Suppose we have a weak pullback (= pseudo-pullback) square of groupoids: G -> H | | v v K -> L Suppose we take presheaves on all four. We can get a square hom(G^{op},Set) -> hom(H^{op},Set) ^ ^ | | hom(K^{op},Set) -> hom(L^{op},Set) where the arrows pointing forward - in the same direction as the original arrows - are defined using pushforward, and the arrows pointing backward are defined using pullback. Does this square commute up to natural isomorphism? Do you know a reference somewhere? Some side remarks: 1) This seems related to the "Beck-Chevalley condition". 2) It may work for categories as well as groupoids, but I happen to need it only for groupoids. 3) I really need it with the category Vect replacing Set, so if you know a general result for any sufficiently nice category playing the role of Set here, that would be wonderful. Best, jb From rrosebru@mta.ca Fri May 4 15:30:29 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 04 May 2007 15:30:29 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1Hk2Qc-0004lx-S7 for categories-list@mta.ca; Fri, 04 May 2007 15:22:50 -0300 Date: Thu, 3 May 2007 13:13:27 -0400 (EDT) From: Michael Makkai To: Categories List Subject: categories: 3rd announcement of (same) paper MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 8 The paper "Computads and 2 dimensional pasting diagrams" has been re-posted on my website http://www.math.mcgill.ca/makkai/. The paper is in a single pdf. It incorporates fresh corrections with respect to the second announcement on April 26th. With greetings: Michael Makkai From rrosebru@mta.ca Fri May 4 15:30:29 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 04 May 2007 15:30:29 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1Hk2PZ-0004gh-G0 for categories-list@mta.ca; Fri, 04 May 2007 15:21:45 -0300 Message-ID: <06ef01c78d6e$cd5a88d0$4601a8c0@RONNIENEW> From: "Ronnie Brown" To: References: Subject: categories: multiple compositions Date: Thu, 3 May 2007 11:35:42 +0100 MIME-Version: 1.0 Content-Type: text/plain;format=flowed; charset="iso-8859-1"; reply-type=original Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 9 Dear Michael, This email is suggested by your announcement at ( http://www.math.mcgill.ca/makkai/) of papers on pasting and computads. First, I hope it is useful to direct people to an early paper with a definition of strict omega-categories, there called \infty-categories: (with P.J. HIGGINS), ``The equivalence of $\infty$-groupoids and crossed complexes'', {\em Cah. Top. G\'eom. Diff.} 22 (1981) 371-386. www.bangor.ac.uk/r.brown/pdffiles/x-comp.pdf The main emphasis of this paper is the equivalence in the title. Because crossed complexes C have a classifying space BC which can also be represented as a fibration over B\pi_1 C with fibre a topological abelian group (in fact the classifying space of a chain complex) this implies that the homotopy type of spaces represented by \infty-groupoids is limited. This observation suggested to Grothendieck in 1982 the need to move to weak \infty-categories (or groupoids) for dealing with matters of nonabelian cohomology, which for him was a long standing aim. It was not till I met him in 1986 that I convinced him that strict n-fold groupoids really did model all weak homotopy n-types, (Loday), at which he exclaimed `That is absolutely beautiful!' There is still work to do on the connections with nonabelian cohomology! And crossed complexes, though limited, are certainly useful for this, because of their close relation to chain complexes with operators. (for a survey on crossed complexes, see math.AT/0212274). Second, I would like to raise some general questions on multiple compositions and what is or should be the mathematics to deal with these. For 2-categories, this seems to be pasting schemes. However the thrust of my work since the 1970s has been to Higher Homotopy van Kampen theorems, (HHvKTs) based on the question of the possible use of groupoids in higher homotopy theory, given their success in 1-dimensional homotopy theory. The key aim was to use cubical methods, because these gave a convenient `algebraic inverse to subdivision', through the use of multiple compositions, modelling steps in the proof of the usual vKT for groupoids. Such HHvKTs were proved with Philip Higgins in dimension 2 in 1978, in all dimensions (for crossed complexes) in 1981, and with Jean-Louis Loday in 1987 (for cat^n groups and so crossed n-cubes of group). All these theorems have algebraic implications for homotopy types which seem unobtainable by other means. The theorems with PJH use directly `algebraic inverse to subdivision', while the proof with Loday uses some sophisticated algebraic topology and simplicial methods (Waldhausen, Zisman, Puppe and some new results). The work obtains to a limited extent a vision of Grothendieck of what he termed `integration of homotopy types'; there are strong connectivity assumptions so the theorems do not allow calculation of everything, e.g. homotopy groups of spheres, and so some have said `the theory has not fullfilled its promise' (report on a failed research proposal). On the other hand, the theory does come within the scope of `higher dimensional nonabelian methods for local-to-global problems', and the new explicit calculations enabled and relations with combinatorial group theory (e.g. the nonabelian tensor product of groups, bibiliography now of 90 items, http://www.bangor.ac.uk/~mas010/nonabtens.html) are pointers to its success. Possibly relevant to this is that I have never been able to write down a proof of even the 2-dimensional HHvKT using 2-groupoids; and it would not have been, or at least was not, even conjectured in those terms. My preference is for algebraic models of homotopy types which lead to some explicit algebraic computations (hence the HHvKTs), to new theorems, and new relations with other areas. My overall questions are therefore: (i) to what extent can and should cubical methods be used in weak category theory? (ii) is there some operadic or other method from current ideas on higher category theory which allows the use of `algebraic inverses to subdivision' in all dimensions? (iii) to what extent are these operadic methods generally useful in higher dimensional nonabelian methods for local-to-global problems? (I first heard of the term local-to-global problems from Dick Swan, when we worked on his lecture notes on the Theory of Sheaves, Oxford, 1958.) Of course subdivision allows the passage from global to local. The problem is the converse, a key problem in maths and science (even biology and engineering!). Anything which helps in this seems to me a Good Thing! Greetings and Good Luck, Ronnie Brown From rrosebru@mta.ca Fri May 4 21:51:02 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 04 May 2007 21:51:02 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1Hk8QP-0002YG-8m for categories-list@mta.ca; Fri, 04 May 2007 21:47:01 -0300 Date: Fri, 4 May 2007 15:50:31 -0400 (EDT) From: Deniz Kural To: categories@mta.ca Subject: categories: Literature on Category Theory and Biology MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 10 Hi, I was wondering if you are aware of any bibliographies, reviews, or papers relating category theory to biology - mathematical biology, systems biology, computational biology or bioinformatics. I would be interested in papers relating category theory to areas of knowledge representation or other areas of computer science used in abovementioned areas. Please feel free to email me in person if you wish not to overburden the mailing list. Regards, Deniz Kural From rrosebru@mta.ca Fri May 4 21:51:02 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 04 May 2007 21:51:02 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1Hk8Ra-0002bP-03 for categories-list@mta.ca; Fri, 04 May 2007 21:48:14 -0300 Subject: categories: Re: Beck-Chevalley for presheaves on groupoids? To: categories@mta.ca Date: Fri, 4 May 2007 17:07:22 -0300 (ADT) MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit From: rjwood@mathstat.dal.ca (RJ Wood) Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: RO X-Status: X-Keywords: X-UID: 11 If G -> H | <= | v v K -> L is a square (with a 2-cell as shown) in cat then applying ^ =((-)^{op},Set) gives G^<- H^ ^ => ^ | | K^<- L^ and taking the mate with respect to the horizontal adjunctions given by left Kan extension gives G^-> H^ ^ => ^ | | K^-> L^ If the original square is a comma square then the 2-cell in the third square is invertible. There are squares other than comma squares, cocomma squares for example, for which the 2-cell in the third square is invertible. See Rene Guitart's early work on exact squares. Best, Rj Wood > One of you must know the answer to this! > > Suppose we have a weak pullback (= pseudo-pullback) square of > groupoids: > > G -> H > | | > v v > K -> L > > Suppose we take presheaves on all four. We can get a square > > hom(G^{op},Set) -> hom(H^{op},Set) > ^ ^ > | | > hom(K^{op},Set) -> hom(L^{op},Set) > > where the arrows pointing forward - in the same direction as > the original arrows - are defined using pushforward, and the arrows > pointing backward are defined using pullback. > > Does this square commute up to natural isomorphism? Do you > know a reference somewhere? > > Some side remarks: > > 1) This seems related to the "Beck-Chevalley condition". > > 2) It may work for categories as well as groupoids, but I happen to > need it only for groupoids. > > 3) I really need it with the category Vect replacing Set, so > if you know a general result for any sufficiently nice category > playing the role of Set here, that would be wonderful. > > Best, > jb From rrosebru@mta.ca Sat May 5 11:46:27 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 05 May 2007 11:46:27 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HkLVO-0001Vr-Tt for categories-list@mta.ca; Sat, 05 May 2007 11:45:02 -0300 Date: Sat, 05 May 2007 10:19:49 +0300 From: Zippie Arzi-Gonczarowski MIME-Version: 1.0 To: categories@mta.ca Subject: categories: Re: Literature on Category Theory and Biology Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 12 Hi, 1.You may want to look at the writings of Robert Rosen (a Google search will provide the necessary links). 2. For a different direction, and on a far more modest note, you may try looking at some of my papers on my web page: http://www.actcom.co.il/typographics/zippie Of course I will be very intrested to hear your comments about that. Good luck, Zippie -- ____________________________________________ Zippora Arzi-Gonczarowski, Ph.D. Aka:Zippie Typographics, Ltd. 46 Hehalutz St. Jerusalem 96222, ISRAEL zippie@actcom.co.il http://www.actcom.co.il/typographics/zippie Tel: +972-2-6437819 Fax: +972-2-6434252 _____________________________________________ From rrosebru@mta.ca Sat May 5 11:46:27 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 05 May 2007 11:46:27 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HkLUI-0001SK-DE for categories-list@mta.ca; Sat, 05 May 2007 11:43:54 -0300 From: Colin McLarty To: categories@mta.ca Date: Fri, 04 May 2007 22:51:39 -0400 MIME-Version: 1.0 Content-Language: en Subject: categories: Re: Literature on Category Theory and Biology Content-Type: text/plain; charset=us-ascii Content-Disposition: inline Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 13 The first time the term "category theory" (I mean, exactly that term) appeared in Mathemtical Reviews was in the review of Rosen, R. [1961]: `A relational theory of the structural changes induced in biological systems by alterations in environment', {\em Bulletin of Mathematical Biophysics} \bf 23}, pp.~165--71. The full review reads: The author uses, among other things, some previous results from his biologico-mathematical applications of abstract category theory [#B416] in order to further develop another paper concerning relational biology [#B418]. Some biological applications are treated; e.g., an interpretation of the mitotic cycle. Rosen's earlier related works are reviewed as dealing with "the theory of categories." best, Colin ----- Original Message ----- From: Deniz Kural Date: Friday, May 4, 2007 8:55 pm Subject: categories: Literature on Category Theory and Biology To: categories@mta.ca > > > Hi, > > I was wondering if you are aware of any bibliographies, reviews, > or papers > relating category theory to biology - mathematical biology, systems > biology, computational biology or bioinformatics. > > I would be interested in papers relating category theory to areas of > knowledge representation or other areas of computer science used in > abovementioned areas. > > Please feel free to email me in person if you wish not to > overburden the > mailing list. > > Regards, > Deniz Kural > > > From rrosebru@mta.ca Sat May 5 11:46:27 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 05 May 2007 11:46:27 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HkLSG-0001Nz-0k for categories-list@mta.ca; Sat, 05 May 2007 11:41:48 -0300 Date: Fri, 4 May 2007 13:37:32 +0200 From: Ralf Treinen To: categories@mta.ca Subject: categories: RDP'07 First Call for Participation Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 14 RDP 2007 - Call for Participation Federated Conference on Rewriting, Deduction, and Programming June 25 to 29, Paris, France http://www.rdp07.org ======================================================================== Online Registration is open unil May, 31. ======================================================================== RDP'07 is the fourth edition of the International Conference on Rewriting, Deduction, and Programming, consisting of two main conferences * Rewriting Techniques and Applications (RTA'07) * Typed Lambda Calculi and Applications (TLCA'07) a colloquium * From Type Theory to Morphologic Complexity: a Colloquium in Honor of Giuseppe Longo as well as the following workshops: * Higher Order Rewriting (HOR) * Proof Assistants and Types in Education (PATE) * Rule-Based Programming (RULE) * Security and Rewriting Techniques (SecReT) * Unification (UNIF) * Functional and (Constraint) Logic Programmming (WFLP) * Reduction Strategies in Rewriting and Programming (WRS) * Termination (WST) Invited Speakers: ================= Joint RTA/TLCA: * Frank Pfenning (Carnegie Mellon University) TLCA: * Patrick Baillot (CNRS, University Paris 13) * Greg Morrisett (Harvard University) RTA: * Xavier Leroy (INRIA Rocquencourt) * Robert Nieuwenhuis (Technical University of Catalonia) Celebratation of the 75th anniversary of the lambda calculus: * Henk Barendregt (Nijmegen University) Registration: ============= http://www.rdp07.org/registration.html Student Travel Grants: ====================== A limited number of travel grants for students is available. A call for applications will be issued separately. Information about travel grants will also be published on http://www.rdp07.org/grants. From rrosebru@mta.ca Sat May 5 21:20:13 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 05 May 2007 21:20:13 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HkUJ3-0006gw-65 for categories-list@mta.ca; Sat, 05 May 2007 21:08:53 -0300 Content-Type: text/plain;charset="us-ascii" Content-Transfer-Encoding: quoted-printable Subject: categories: Re: Literature on Category Theory and Biology Date: Sat, 5 May 2007 11:44:43 -0400 From: "Wojtowicz, Ralph" To: Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 15 The links: http://perso.orange.fr/vbm-ehr/ and=20 http://alf.nbi.dk/%7Eemmeche/coPubl/97d.NABCE/ExplEmer.html =20 and a related paper "Categorical language and hierarchical models for cell systems" by R. Brown, R. Paton and T. Porter may be of interest. I believe that Brown and Porter have other references of this nature. See also the recent work by M. Healy on neural networks. Best wishes, Ralph Wojtowicz wojtowicz@metsci.com From rrosebru@mta.ca Sat May 5 21:20:13 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 05 May 2007 21:20:13 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HkUK7-0006jZ-Sj for categories-list@mta.ca; Sat, 05 May 2007 21:09:59 -0300 Date: Sat, 05 May 2007 18:42:30 +0200 From: Andree Ehresmann To: categories@mta.ca Subject: categories: Re: Literature on Category Theory and Biology MIME-Version: 1.0 Content-Type: text/plain;charset=ISO-8859-1;DelSp="Yes";format="flowed" Content-Disposition: inline Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 16 In answer to Deniz Kural With Jean-Paul Vanbremeersch we have been developing a model for biological and neural systems based on category theory called Memory Evolutive Systems. Since 20 years we have published a series of papers on this subject, most of which are posted on our Internet site http://perso.wanadoo.fr/vbm-ehr Recently we have written a book on this subject: Memory Evolutive sytems: hierarchy, emergence, cognition" due to appear this month in the series "Studies in Multidisciplinarity" of Elsevier (volume 4). Sincerely Andree C. Ehresmann From rrosebru@mta.ca Sat May 5 21:26:31 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 05 May 2007 21:26:31 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HkUYY-0007Nx-2C for categories-list@mta.ca; Sat, 05 May 2007 21:24:54 -0300 From: "David Ellerman" To: Subject: categories: Re: Literature on Category Theory and Biology Date: Sat, 5 May 2007 09:01:45 -0700 MIME-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 17 A new "heteromorphic" treatment of adjoint functors provides applications to biology such as an abstract characterization of selectionist (as opposed to instructionist) mechanisms as in Darwin's evolutionary theory, the selectionist theory of the immune system, and neural darwinism (e.g., Edelman's and Changeux's work). Heteromorphisms, e.g., the injection of a set of generators into the free group on the set, can be formally treated in category theory using bifunctors Het:X^op x A--> Set analogous to the usual Hom:X^op x X-->Set. When the heteromorphisms from objects in a category X to objects in a category A can represented in each of the categories, then the functors giving the representing objects are a pair of adjoint functors and the representations give a pair of natural isomorphisms: Hom_A(Fx,a) = Het(x,a) = Hom-_X(x,Ga). The usual treatment of adjoints leaves out the middle term. And all adjoint functors can be shown to arise in this manner (up to isomorphism). The applications were not available in the usual treatment of adjoints where the heteromorphisms were not explicit. The applications are outlined in a paper just published in Axiomathes (2007) 17: 19-39. A reprint can be retreived from my website: http://www.ellerman.org/Davids-Stuff/Maths/Adjoints-Axiomathes-Reprint.pdf . A rather long (and impenetrable) treatment of the math was in the recent "What is Category Theory" collection of papers (2006: Polimetrica). A short straightforward treatment of the math is available on the ArXiv: http://arxiv.org/abs/0704.2207v1 . Other applications of category theory to biology have been made by Robert Rosen (as mentioned by several posts) and by Andree Ehresmann. Best, David __________________ David Ellerman Visiting Scholar University of California at Riverside Email: david@ellerman.org Webpage: www.ellerman.org View my research on my SSRN Author page: http://ssrn.com/author=294049 From rrosebru@mta.ca Mon May 7 10:07:59 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 07 May 2007 10:07:59 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1Hl2lr-0003tr-6b for categories-list@mta.ca; Mon, 07 May 2007 09:56:55 -0300 Mime-Version: 1.0 (Apple Message framework v752.2) Content-Type: text/plain; charset=ISO-8859-1; delsp=yes; format=flowed Content-Transfer-Encoding: quoted-printable From: Francois Lamarche Subject: categories: PSSL 86 in Nancy: Preliminary Announcement Date: Mon, 7 May 2007 13:16:00 +0200 To: categories@mta.ca Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 18 Fellow category theorists, The 86th edition of the Peripatetic Seminar on Sheaves and Logic will =20= be held at the Institut =C9lie Cartan of the Universit=E9 Henri Poincar=E9= =20 in Nancy, on the weekend of September 8-9 2007. More details will be announced later this summer, but interested =20 people can start contacting me now. We intend to continue the PSSL =20 tradition of informality, and scheduling talks pertaining to any =20 aspect of category theory, with or without applications in natural =20 science, logic, computer science, or other branches of mathematics. The fast TGV-Est train line will be inaugurated in June, and the =20 Paris-Nancy trip will then take only 1h30m, with easy connections to =20 the two Paris airports. The city of Nancy is right on the Paris-=20 Munich train line, and also has good train connecftions with the =20 north (Luxembourg, Brussels and Frankfurt via Metz) and the south =20 (Lyon, Nice...). There is a local airport, 45 minutes away from =20 downtown by minibus shuttle, and there are also two relatively close =20 international airports, Luxembourg and Strasbourg, which often allow =20 you to do the airport-dowtown Nancy trip in less than 2h30m. Nancy is of considerable interest for the mathematical tourist, being =20= the birthplace of Henri Poincar=E9, and being intimately related to the =20= career of Nicolas Bourbaki. It has two historical old towns: the =20 medieval one, with the Renaissance palace of the Dukes of Lorraine, =20 and the classical one, with UNESCO World heritage sites built by Duke =20= Stanislas. It is can also boast one of the highest concentrations of =20 Art Nouveau architecture in all of Europe, rivalling Prague and =20 Barcelona. Hoping to see you in September, Fran=E7ois Lamarche http://www.loria.fr/~lamarche From rrosebru@mta.ca Mon May 7 19:47:28 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 07 May 2007 19:47:28 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HlBuT-0004lT-2z for categories-list@mta.ca; Mon, 07 May 2007 19:42:25 -0300 Date: Mon, 7 May 2007 13:03:27 -0600 (MDT) Subject: categories: Re: Literature on Category Theory and Biology From: mjhealy@ece.unm.edu To: categories@mta.ca MIME-Version: 1.0 Content-Type: text/plain;charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 19 Regarding Deniz Kural's question about references to papers on category theory and biology, Tom Caudell and I have been investigating a semantic theory for neural networks both biological and artificial, cognitive and non-cognitive. We are designing and conducting experiments to test and refine the theory in both neuroscience and cognitive psychology working with colleagues in those disciplines. An initial paper on the theory is M. J. Healy and T. P. Caudell (2006) Ontologies and Worlds in Category Theory: Implications for Neural Systems= , Axiomathes, vol. 16, nos. 1-2, pp. 165-214. The only experiment appearing in a publication to date is one on an artificial neural network application, presented at IJCNN 2005 in Montrea= l (the results were presented also at CT06). Regards, Mike Healy From rrosebru@mta.ca Wed May 9 09:21:25 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 09 May 2007 09:21:25 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1Hll1k-0002Qs-Jx for categories-list@mta.ca; Wed, 09 May 2007 09:12:16 -0300 Date: Wed, 9 May 2007 08:17:38 GMT From: Jeremy.Gibbons@comlab.ox.ac.uk To: categories@mta.ca Subject: categories: Integrated Formal Methods 2007: Call for participation Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 20 IFM2007: INTEGRATED FORMAL METHODS CALL FOR PARTICIPATION 2nd to 5th July 2007 St Anne's College, Oxford, UK www.ifm2007.org The design and analysis of computing systems presents a significant challenge: systems need to be understood at many different levels of abstraction, and examined from many different perspectives. Formal methods - languages, tools, and techniques with a sound, mathematical basis - can be used to develop a thorough understanding, and to support rigorous examination. Further research into effective integration is required if these methods are to have a significant impact outside academia. The IFM series of conferences seeks to promote that research, to bring together the researchers carrying it out, and to disseminate the results of that research among the wider academic and industrial community. This is the sixth IFM conference. It will be held in the historic university town of Oxford, at St Anne's College - one of the larger colleges of the University, with excellent new conference facilities. Oxford is easily reached from most UK cities, and is 70 minutes from the country's largest airport. Earlier conferences in the series were held at York (1999), Schloss Dagstuhl (2000), Turku (2002), Kent (2004), and Eindhoven (2005). The conference runs for three full days, 3rd to 5th July. Invited speakers include Jifeng He on "UTP Semantics for Web Services" and Daniel Jackson on "Recent Advances in Alloy"; a third invited speaker is yet to be confirmed. There are 32 contributed papers, including a special session on Unifying Theories of Programming. In addition, there are four satellite events, taking place on 2nd and 3rd July - three workshops: * Refinement Workshop * C/C++ Verification * MeMoT (Methods, Models and Tools for Fault Tolerance) and a tutorial: * KeY (Integrating OO Design and Deductive Verification of Software) The full programme is available at: http://www.ifm2007.org/programme-ifm.html Registration for the conference is now open, at: http://www.ifm2007.org/registration.html Special early-registration fees apply until 1st June 2007. For more information, visit the conference web page: http://www.ifm2007.org/ or contact the local organisers: Jim Davies http://www.softeng.ox.ac.uk/Jim.Davies Jeremy Gibbons http://www.softeng.ox.ac.uk/Jeremy.Gibbons From rrosebru@mta.ca Wed May 9 09:21:25 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 09 May 2007 09:21:25 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1Hll85-0002st-Ns for categories-list@mta.ca; Wed, 09 May 2007 09:18:49 -0300 From: Marco Grandis Subject: categories: The policy of arXiv Date: Wed, 9 May 2007 11:40:48 +0200 To: LIBGATEWAY-L@cornell.edu, categories@mta.ca Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 21 Dear Sirs, Before deciding of using arXiv in a systematic way, I would like that =20= there be a clear statement of its policy and commitments; a statement =20= which, likely, the organisers and many of us take as understood and =20 granted, but which I have been unable to find. To be more explicit, what about the possibility of the system being, =20 in future, exploited economically? What about the possibility of it =20 being sold to a commercial company? When downloading an article to the arXiv, the author is asked to =20 grant 'a perpetual, non-exclusive license to distribute this =20 article'. I think the author has a right to know that this license =20 will not be used, in the future, for goals which would be in contrast =20= with the present (understood) ones, or even opposite to them. Last year I wrote a message in this sense to the list =20 'categories' (categories@mta,ca), where arXiv has been frequently =20 proposed as a way of disseminating articles. In December 2006 there =20 was a discussion about these points in a blog kept by John Baez http://golem.ph.utexas.edu/category/2006/12/=20 arxiv_policy_statement.html This is part of a posting by John Baez, on this blog: "Many people like to have some idea of what an organization seeks to =20 do, or is committed to do, before they do business with it. For this reason, it=92s unusual for such an important entity as the =20 arXiv not to make a public statement about its goals and commitments. =20= Consider, for example, the Berlin Declaration on Open Access to =20 Knowledge in the Sciences and Humanities, and its many signatories, =20 or the statement by the Wellcome Trust supporting open access, or the =20= Wikimedia mission statement and bylaws, or the Google code of conduct =20= and privacy policy. " (end of citation) As far as I know, there still is no policy statement available. One =20 can only read, at the head of the 'arXiv Advisory Board' page: "Please note that all arXiv policy decisions are ultimately made by =20 Cornell University Library." Will the Cornell University Library make its arXiv policy public? With best regards Marco Grandis Dipartimento di Matematica Universit=E0 di Genova Via Dodecaneso, 35 16146 Genova Italy e-mail: grandis@dima.unige.it tel: +39 010 353 6805 http://www.dima.unige.it/~grandis/= From rrosebru@mta.ca Thu May 10 08:40:17 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 10 May 2007 08:40:17 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1Hm6ub-0002kq-94 for categories-list@mta.ca; Thu, 10 May 2007 08:34:21 -0300 Date: Wed, 9 May 2007 07:35:28 -0700 (PDT) From: Bill Rowan To: categories@mta.ca Subject: categories: Re: The policy of arXiv MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: RO X-Status: X-Keywords: X-UID: 22 Hi all, I think it is relevant to point out that if people who post articles to the Arxiv agree to grant a permanent, _non-exclusive_ right to distribute the article, that means, that if the operators of the Arxiv, whoever they are, decide to sell copies of the database, or individual articles, they won't be entitled to prevent anyone else from distributing the same material for free. So they can't corner the market on the content, in other words. All in all it doesn't seem that big of a concern to me, although certainly worth a thoughtful discussion. It would be nice to hear from Cornell Library about their intentions. Bill Rowan From rrosebru@mta.ca Fri May 11 20:30:01 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 11 May 2007 20:30:01 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HmeOz-0006Ti-UJ for categories-list@mta.ca; Fri, 11 May 2007 20:19:57 -0300 From: "Philip Mulry" To: categories@mta.ca Subject: categories: FMCS 2007 - Final Call for Participation Date: Fri, 11 May 2007 13:59:55 -0400 MIME-Version: 1.0 Content-Type: text/plain;charset="iso-8859-1" Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 23 **************************************************** Final Announcement - FMCS 2007 This is the final call for participation in FMCS 2007 *** The registration deadline is May 20. *** University accommodations can not be guaranteed after that date. The Department of Computer Science at Colgate University is hosting Foundational Methods in Computer Science 2007 on the Colgate University campus in Hamilton N.Y. Dates: Arrival on Thursday June 7, 2007 (Reception in the evening). Scientific Program Friday June 8 - Sunday June 10 (ends mid-day). The workshop is an annual meeting meant to bring together researchers in mathematics and computer science with a focus on the application of category theory in computer science. The meeting will begin with a day of research tutorials, followed by a day and a half of research talks. Invited speakers this year include: a.. Steve Awodey(Carnegie Mellon) b.. Steve Bloom(Stevens) c.. Robin Cockett (Calgary) d.. Paul Hudak(Yale) e.. Ernie Manes (U Mass) f.. Robert Rosebrugh(Mount Allison) The remaining research talks are solicited from participants. Time slots are limited, so please register early if you would like to be considered for a talk. Graduate student participation is particularly encouraged at FMCS 2007. Students will pay a reduced registration fee. Conference Link: http://cs.colgate.edu/faculty/mulry/FMCS2007/FMCS2007.html Contacts The local organizer of FMCS 2007 is: Philip Mulry The secretary for FMCS 2007 is Char Jablonski From rrosebru@mta.ca Sat May 12 19:50:22 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 12 May 2007 19:50:22 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1Hn0Iu-0007R2-Df for categories-list@mta.ca; Sat, 12 May 2007 19:43:08 -0300 Date: Sat, 12 May 2007 10:51:10 -0300 (BRT) Subject: categories: WoLLIC'2007 - Call for Participation From: ruy@cin.ufpe.br To: wollic@cin.ufpe.br MIME-Version: 1.0 Content-Type: text/plain;charset=iso-8859-1 Content-Transfer-Encoding: 8bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 24 [** sincere apologies for duplicates **] Call for Participation 14th Workshop on Logic, Language, Information and Computation (WoLLIC'2007) Rio de Janeiro, Brazil July 2-5, 2007 (a satellite event to Brazilian Computer Society Conference - CSBC'07) WoLLIC is an annual international forum on inter-disciplinary research involving formal logic, computing and programming theory, and natural language and reasoning. Each meeting includes invited talks and tutorials as well as contributed papers. The Fourteenth WoLLIC will be held in Rio de Janeiro, Brazil, from July 2 to July 5, 2007, in conjunction with the 27th Brazilian Computer Society Conference. It is sponsored by the Association for Symbolic Logic (ASL), the Interest Group in Pure and Applied Logics (IGPL), the European Association for Logic, Language and Information (FoLLI), the European Association for Theoretical Computer Science (EATCS), the Sociedade Brasileira de Computacao (SBC), and the Sociedade Brasileira de Logica (SBL). PROCEEDINGS The proceedings of WoLLIC'2007, including both invited and contributed papers, will be published in advance of the meeting as a volume in Springer's Lecture Notes in Computer Science. In addition, abstracts will be published in the Conference Report section of the Logic Journal of the IGPL, and selected contributions will be published as a special post-conference WoLLIC'2007 special issue of the journal Information and Computation. INVITED SPEAKERS Alex Borgida (Rutgers) Alessandra Carbone (Paris) Martin Escardo (Birmingham) Philippa Gardner (Imperial Coll) Achim Jung (Birmingham) Louis Kauffman (U Illinois Chicago) Michael Moortgat (Utrecht) Paulo Oliva (London/QM) John Reif (Duke) Yde Venema (Amsterdam) TUTORIAL LECTURES Stone duality, by A. Jung Quantum topology and quantum computation, by L. Kauffman Biological computing, by J. Reif INVITED TALKS Description Logics: formal foundations and applications, by A. Borgida Group Theory and Classical Proofs, by A. Carbone Algorithmic Topology of Program Types, by M. Escardo Contex Logic and Tree Update, by Ph. Gardner On the interplay of logic and information: A topological analysis, by A. Jung Spin networks in quantum computation, by L. Kauffman Symmetries in natural language syntax and semantics: the Lambek-Grishin calculus, by M. Moortgat Computational Interpretations of Classical Linear Logic, by P. Oliva Autonomous programmable biomolecular devices using self-assembled DNA nanostructures specifying properties of data DNA Nanostructures, by J. Reif A modal distributive law, by Y. Venema BOOK EXHIBITION The following publishers are expected to be exhibiting various books from their catalogue, prospectuses, journal samples, etc., and there will be a chance to order items at promotional prices: The MIT Press Springer-Verlag A K Peters Cambridge Univ Press CSLI Publications (Stanford Univ) Oxford Univ Press World Scientific It is likely that a few other international publishers will also take part in the book exhibit. PROGRAM COMMITTEE Samson Abramsky (U Oxford) Michael Benedikt (Bell Labs) Lars Birkedal (ITU Copenhagen) Andreas Blass (U Michigan) Thierry Coquand (Chalmers U, Goteborg) Jan van Eijck (CWI, Amsterdam) Marcelo Finger (U Sao Paulo) Rob Goldblatt (Victoria U, Wellington) Yuri Gurevich (Microsoft Redmond) Hermann Haeusler (PUC Rio) Masami Hagiya (Tokyo U) Joseph Halpern (Cornell U) John Harrison (Intel UK) Wilfrid Hodges (U London/QM) Phokion Kolaitis (IBM Almaden Research Center) Marta Kwiatkowska (U Birmingham) Daniel Leivant (Indiana U) (Chair) Maurizio Lenzerini (U Rome) Jean-Yves Marion (LORIA Nancy) Dale Miller (Polytechnique Paris) John Mitchell (Stanford U) Lawrence Moss (Indiana U) Peter O'Hearn (U London/QM) Prakash Panangaden (McGill, Montreal) Christine Paulin-Mohring (Paris-Sud, Orsay) Alexander Razborov (Steklov, Moscow) Helmut Schwichtenberg (Munich U) Jouko Vaananen (U Helsinki) ORGANISING COMMITTEE Marcelo da Silva Correa (U Fed Fluminense) Renata P. de Freitas (U Fed Fluminense) Ana Teresa Martins (U Fed Ceara') Anjolina de Oliveira (U Fed Pernambuco) Ruy de Queiroz (U Fed Pernambuco, co-chair) Petrucio Viana (U Fed Fluminense, co-chair) WEB PAGE www.cin.ufpe.br/~wollic/wollic2007 --- From rrosebru@mta.ca Mon May 14 12:35:31 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 14 May 2007 12:35:31 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HncOj-00005X-Jz for categories-list@mta.ca; Mon, 14 May 2007 12:23:41 -0300 Mime-Version: 1.0 (Apple Message framework v752.3) Content-Type: text/plain; charset=US-ASCII; format=flowed Content-Transfer-Encoding: 7bit From: Ross Street Subject: categories: An obituary for Max Date: Mon, 14 May 2007 15:44:55 +1000 To: Categories Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 25 See the latest issue of the Aust Math Soc Gazette Ross From rrosebru@mta.ca Tue May 15 08:33:29 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 15 May 2007 08:33:29 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HnvAV-0004ep-9J for categories-list@mta.ca; Tue, 15 May 2007 08:26:15 -0300 Mime-Version: 1.0 Date: Mon, 14 May 2007 14:48:49 +0200 To: categories@mta.ca From: Michal Walicki Subject: categories: CALCO-07 - Call for Participation Content-Type: text/plain; charset="iso-8859-1" ; format="flowed" Content-Transfer-Encoding: quoted-printable Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 26 CALCO 2007 2nd Conference on Algebra and Coalgebra in Computer Science CALCO Tools Day August 20-24, 2007, Bergen, Norway May 16 Early Registration deadline July 1 Registration deadline ------------------------------------------------------------------ http://www.ii.uib.no/calco07/ ------------------------------------------------------------------ August 20 CALCO-jnr, CALCO-tools August 21-24 CALCO technical programme CALCO'07 takes place at the Grand Hotel Terminus in Bergen, one of many historic hotels in Norway. The conference starts Monday with two workshops followed by an official reception Monday evening. The main program runs Tuesday through Friday, each morning starting with an invited speaker. Additional events are excursion by boat in the Bergen archipelago (Wednesday afternoon) and conference dinner on one of the mountains surrounding the city centre (Thursday afternoon). Registration ------------ Registration fee is 3200 NOK (1200 NOK for students), with substantial discounts for early registration. The fee includes the full conference with all workshops, a copy of the proceedings,=20 lunches and coffee breaks, internet access and=20 the official reception Monday evening. Registration is via the calco07 web site: http://www.ii.uib.no/calco07/ Note that Bergen is very busy during the tourist season, so early booking of accommodation and transportation is recommended. Main CALCO'07 conference ------------------------ CALCO is a high-level, bi-annual conference. It brings together researchers and practitioners to exchange new results related to foundational aspects and both traditional and emerging uses of algebras and coalgebras in computer science. The study of algebra and coalgebra relates to the data, process and structural aspects of software systems. The accepted papers report results of theoretical work on the mathematics of algebras and coalgebras, the way these results can support methods and techniques for software development, as well as experience with the transition of resulting technologies into industrial practise. Some main key words are: * Abstract models and logics * Specialised models and calculi * Algebraic and coalgebraic semantics * System specification and verification The list of accepted papers is available at the web site. Invited speakers ---------------- Stephen L. Bloom, Stevens Institute of Technology, NJ, USA Prof. Bloom works on algebraic specification theories and was instrumental in developing iterative theories, an elaborate coalgebraic method - predating coalgebras. Luis Caires, New University of Lisbon, Portugal Prof. Caires has made important contributions to the field of distributed and mobile systems, and spatial logics for these. Barbara K=88=8Fnig, University of Duisburg-Essen, Germany Prof. K=88=8Fnig works on graph transformation systems, with applications to concurrent and mobile systems, software reliability and security. Glynn Winskel, University of Cambridge, United Kingdom Prof. Winskel is well-known for his fundamental work in semantics and theory of concurrency. CALCO-jnr (CALCO Young Researchers Workshop) -------------------------------------------- CALCO-jnr is dedicated to presentations by PhD students and by those who completed their doctoral studies within the past few years. This year 12 contributions within the theme of CALCO have been accepted. See the overview on the CALCO-jnr web page on the CALCO web site. -- http://www.ii.uib.no/calco07/ From rrosebru@mta.ca Sat May 19 10:48:06 2007 -0300 Status: X-Status: X-Keywords: Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 19 May 2007 10:48:06 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HpP7T-0000IX-U9 for categories-list@mta.ca; Sat, 19 May 2007 10:37:16 -0300 Date: Fri, 18 May 2007 12:52:13 -0500 (CDT) From: MYV To: vardi@cs.rice.edu Subject: categories: Book - Finite Model Theory and Its Applications Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Finite Model Theory and Its Applications by Erich Graedel, Phokion G. Kolaitis, Leonid Libkin, Maarten Marx, Joel Spencer, Moshe Y. Vardi, Yde Venema, and Scott Weinstein Springer, 2007, 437 pages, hardcover, ISBN: 978-3-540-00428-8. (Series: Texts in Theoretical Computer Science. An EATCS Series) >From the back cover: This book gives a comprehensive overview of central topics in finite model theory - expressive power of logics, descriptive complexity, and zero-one laws - together with selected applications relating to database theory and artificial intelligence, especially constraint databases and constraint satisfaction problems. The final chapter provides a concise modern introduction to modal logic, emphasizing the interaction with finite model theory. The underlying theme of the book is the use of first-order, second-order, fixed-point, and infinitary logic, as well as various fragments of and hierarchies within these logics, to gain insight into phenomena and problems in complexity theory and combinatorics. The book emphasizes the use of combinatorial games, such as extensions and refinements of the Ehrenfeucht-Fraissi games, as a powerful way to analyze the expressive power of logics, and illustrates how sophisticated notions from model theory and combinatorics, such as o-minimality and treewidth, arise naturally in the applications of finite model theory to database theory and artificial intelligence. Students of logic and computer science will find here the tools necessary to embark on research into finite model theory, and all readers will experience the excitement of a vibrant area of the applications of logic to computer science. Table of contents: 1.Unifying Themes in Finite Model Theory 2.On the Expressive Power of Logics on Finite Models 3.Finite Model Theory and Descriptive Complexity 4.Logic and Random Structures 5.Embedded Finite Models and Constraint Databases 6.A Logical Approach to Constraint Satisfaction 7.Local Variations on a Loose Theme: Modal Logic and Decidability To order, see http://www.springer.com/978-3-540-00428-8 From rrosebru@mta.ca Wed May 23 07:09:42 2007 -0300 Status: X-Status: X-Keywords: Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 23 May 2007 07:09:42 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1Hqncp-0001Qe-RU for categories-list@mta.ca; Wed, 23 May 2007 06:59:23 -0300 Date: Wed, 23 May 2007 08:47:43 +0100 From: Alexander Kurz MIME-Version: 1.0 To: categories Subject: categories: hyperdoctrines and cylindric algebras Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: There clearly is a connection between hyperdoctrines and cylindric algebras. Does anybody knows work that relates the two? Or that makes use of a result from one area to prove something in the other? I would be greatful for any reference or comment. Best wishes, Alexander From rrosebru@mta.ca Thu May 24 08:04:53 2007 -0300 Status: X-Status: X-Keywords: Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 24 May 2007 08:04:53 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HrAzS-0007Dr-UT for categories-list@mta.ca; Thu, 24 May 2007 07:56:18 -0300 Date: Thu, 24 May 2007 00:46:38 -0400 From: "Zinovy Diskin" Subject: categories: Re: hyperdoctrines and cylindric algebras To: categories MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: On 5/23/07, Alexander Kurz wrote: > There clearly is a connection between hyperdoctrines and cylindric > algebras. > yes, of course. Roughly speaking, they are equivalent: hyperdoctrines (HDs) are indexed category style algebraization of first order logic while cylindric algebras (CAs) are an equivalent fibrational formulation. To make it precise, we need to consider a few rather straightforward yet technically bulky generalizations of both notions, reproducing in HDs the classical context of CAs and vice versa. I'm traveling and do not have references at hand, but below is an outline of how it can be done (apologies for possible inaccuracies). > Does anybody knows work that relates the two? Or that makes use of a > result from one area to prove something in the other? > The last question is interesting. If we are speaking about pure algebra, there is nothing exciting in "switching" between HDs and CAs: these are just different representation of the same algebraic theory. More accurately, HDs are equivalent to locally finite CAs, which are not equationally definable. Thus, HDs are much more manageable algebraically (but many-sorted). This trade-off between number of sorts and equational definability is probably the most/only interesting algebraic point. However, the main driving force of CA development was in the representation theorems, which are for CAs are much more intricate than Stone representation theorems for Boolean algebras. In the companion volume to the classical monograph by Henkin, Monk,Tarsky (where the great trio is joined by Andreka & Nemeti), there is a lot of interesting and not-easy-to-prove representation theorems (googling Andreka-Nemeti should provide references). I'm not aware of any similar results (or even interest in such results) for HDs. ZD == 8< == equivalence of HDs and CAs: a rough outline Let's fix a countable set V (of variables). Consider a simple version of the notion of hyperdoctrine, p:T-->BA^op is an indexed cat, where T=Pow_fin(V) is the category of finite subsets of V and mappings between them and BA is the category of Boolean algebras. Now we apply to p the Grothendieck construction and get a fibration \delta: G-->T. A straitforward check shows that G is a locally finite cylindric algebra (CA). (Special axioms regulating interactions of substitutions and bound variables hold because of Beck-Chevalle and Frobenius conditions). Conversely, if A is a locally finite cylindric algebra over V and a\in A, define \delta(a) = {x \in V| C_x(a) not= a} (C_x is cylindrification operator/quantifier). As a Boolean algebra, A is an order category and \delta is a fibration. Its indexed version gives an HD over a trivial algebraic theory (and with Boolean fibres). To get an equivalence result for non-trivial algebraic theories, the notion of CA over a variety was introduced (first by Boris Plotkin for Halmos' polyadic algebras, and then by Janis Cirulis for CAs). To extend equivalence for the classical HDs where fibres are intuitionistic, we need the notion of cylindric Heyting algebras. To extend the equivalence for CAs that are not locally finite, we need HDs over Ts being cats with any products (not necessary finite). Another version of equivalence results can be obtained if we replace CAs by polyadic algebras introduced by Halmos. One more delicate point is that CAs are equivalent to polyadic algebras with equality while there are also polyadic algebras without equality. Such things were popular at Riga algebraic seminar about twenty years ago. I think that then I wrote a preprint where all this was carefully formulated; hopefully, I still have a hard copy (never thought that anybody would need it :). > I would be greatful for any reference or comment. > > Best wishes, > > Alexander > > > > From rrosebru@mta.ca Thu May 24 08:04:54 2007 -0300 Status: X-Status: X-Keywords: Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 24 May 2007 08:04:54 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HrAwC-000774-RE for categories-list@mta.ca; Thu, 24 May 2007 07:52:56 -0300 To: LICS List From: Kreutzer + Schweikardt Subject: categories: LICS 2007 - Call for Participation Date: Wed, 23 May 2007 12:48:42 +0200 (CEST) Sender: cat-dist@mta.ca Precedence: bulk Message-Id: LICS 2007 Call for Participation Reminder: Early registration deadline is approaching: May 31st, 2007 LICS 2007 will be held in the Institute of Computer Science, University of Wroclaw, Poland, 10th - 14th July 2007. It will be colocated with: - International Colloquium on Automata, Languages and Programming (ICALP 2007), 9th - 13th July 2007, and - ASL European Summer Meeting (Logic Colloquium 2007), 14th - 19th July 2007. The IEEE Symposium On Logic In Computer Science (LICS) is an annual international forum on theoretical and practical topics in computer science that relate to logic broadly construed. Detailed information can be found on the webpage: - http://www.informatik.hu-berlin.de/lics/lics07/ - http://july2007.ii.uni.wroc.pl/ Important dates: - May 31st 2007: Early registration discount expires. - 10th - 14th July 2007: Conference Invited Speakers: - Thomas Hales (University of Pittsburgh) - Martin Hyland (University of Cambridge) - Phokion Kolaitis (IBM Almaden Research Centre) - Gordon Plotkin (University of Edinburgh) - Michael Rabin (Harvard University and Hebrew University) - Colin Stirling (University of Edinburgh) From rrosebru@mta.ca Tue May 29 06:08:13 2007 -0300 Status: X-Status: X-Keywords: Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 29 May 2007 06:08:13 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HsxfH-0000eq-8S for categories-list@mta.ca; Tue, 29 May 2007 06:06:51 -0300 Date: Mon, 28 May 2007 16:03:49 -0400 (EDT) From: Bill Lawvere To: categories Subject: categories: Re: hyperdoctrines and cylindric algebras (Correction) MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Hyperdoctrines (in many variants) were introduced as an algebraic aspect of "proof theory" and as such are definitely not equivalent to cylindric algebras (or polyadic algebras or even various categorical formulations of logic). They involve fibered categories whose fibers are cartesian closed (and with adjoints between the fibers etc.). The poset reflection of these fibers are Heyting algebras. This reflection process was intuited already by Curry and was later called "the Curry-Howard isomorphism" even though this is a serious misnomer because it is very far from being an isomorphism. (See my paper Adjoints in and among bi-categories, Logic & Algebra, Lecture Notes in Pure and Applied Mathematics. 180:181-189. Ed. A. Ursini, P Agliano, Marcel Dekker, Inc. Basel, 1996, as well as the author's commentary on my paper Adjointness in Foundations, as reprinted in TAC. Recent papers of Matias Menni further clarify these developments, which were partly inspired by work of Hans Laeuchli.) Conceptually, the problem of presentation of a theory in algebraic logic by means of primitive predicates and axioms can be viewed as taking place in two steps: first the presentation of a hyperdoctrine with non-trivial fibers, and then the further collapse by imposing the condition that projection maps act as inverse to diagonal maps (within each fiber). This process can be localized. The problematic existential quantifier which is the core problem of proof theory: ("there exists a proof of ....") is thus split into several parts to be studied separately. I hope the above helps to clarify the relationship between two levels of categorical algebra. Bill ************************************************************ F. William Lawvere, Professor emeritus Mathematics Department, State University of New York 244 Mathematics Building, Buffalo, N.Y. 14260-2900 USA Tel. 716-645-6284 HOMEPAGE: http://www.acsu.buffalo.edu/~wlawvere ************************************************************ On Thu, 24 May 2007, Zinovy Diskin wrote: > On 5/23/07, Alexander Kurz wrote: > > There clearly is a connection between hyperdoctrines and cylindric > > algebras. > > > > yes, of course. Roughly speaking, they are equivalent: hyperdoctrines > (HDs) are indexed category style algebraization of first order logic > while cylindric algebras (CAs) are an equivalent fibrational > formulation. To make it precise, we need to consider a few rather > straightforward yet technically bulky generalizations of both notions, > reproducing in HDs the classical context of CAs and vice versa. I'm > traveling and do not have references at hand, but below is an outline > of how it can be done (apologies for possible inaccuracies). > ... From rrosebru@mta.ca Thu May 31 07:48:20 2007 -0300 Status: X-Status: X-Keywords: Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 31 May 2007 07:48:20 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1Hti2X-0000H7-Qt for categories-list@mta.ca; Thu, 31 May 2007 07:37:57 -0300 Date: Tue, 29 May 2007 10:37:00 -0400 From: "Zinovy Diskin" Subject: categories: Re: hyperdoctrines and cylindric algebras (Correction) To: categories MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Content-Disposition: inline Sender: cat-dist@mta.ca Precedence: bulk Message-Id: I'm afraid that still some clarification is needed. Standard hyperdoctrines (HDs) and standard cylindric algebras (CAs) are not equivalent by the following two groups reasons. (1) How we model logic/predicates. In HDs, objects in fibers are predicates of finite arities, the logic is intuitionistic and we are interested in proofs (arrows) rather than just provability (partial order). In CAs (of dimension \alpha = enumeration of some predefined set of variables), elements are to be thought of as predicates of arity \alpha, the logic is classical and we are interested in the partial order of provability (CAs are Boolean algebras with an extra structure). (2) How we model algebra/terms. In an HD T-->Cat^op, the algebraic base T is an *arbitrary* finitary algebraic theory. In CAs, the algebraic base is *the trivial* finitary algebraic theory over \alpha, whose only operations are projections. The difference is quite evident , and I believe that the actual question was not about the difference but rather about how to figure out the commonalities (and formulate equivalence if it can be formulated). Result 1: adjusting HDs to CAs and PAs (polyadic algebras). The following three notions are equivalent: -- locally finite CA (of dimension \omega), -- locally finite PA with equality, -- HD, whose fibers are Boolean algebras and the algebraic base has no morphisms other than projections. The condition of being locally-finite can be removed if we define HDs over algebraic bases having countable (rather than just finite) products. Result 2: adjusting CAs/PAs to HDs. The following three notions are equivalent: -- HD, whose fibers are posets, -- locally finite "polyadic Heyting algebra" with equality over a variety, -- locally finite "cylindric Heyting algebra" over a variety. Many similar equivalence results in-between and around the two above can be formulated. Roughly, anything that can be defined for poset HDs in the fibred fashion, can be reproduced for CA/PAs in the globalistic fashion (via the Grothendieck construction) and vice versa. However, the HD formalism is much more flexible as can be seen already from the two results above. Result 1 is conceptually and technically easy. Result 2 is equally easy conceptually but is much more intricate technically. Defining polyadic Heyting algebras needs a certain technical work, which is essentially nothing but reproducing the basic Lawvere's observation of quantifiers as adjounts in the global Heyting algebra setting. In general, the notion of CA of an infinite dimension is conceptually messy: elements are predicates of infinite arities while quantifiers and variable substitutions are finitary (and even worse, substitutions are not a basic notion and need to be derived via diagonals, see Janis Cirulis' papers. But once again, the main concern of developing CAs was to algebraize semantics -- algebras of relations, rather than syntax and proof theory). Halmos' polyadic algebras are conceptually more consistent in this sense (and probably because in their design the syntactical side was taken more seriously) . Despite all these technical differences, HDs are CAs/PAs are close in the sense that they both follow the same basic idea of algebraizing logic: the algebras are generated by signatures and axioms (theories). In a bit more detail: a signature \Sigma of operation and predicate symbols of finite arities freely generates an HD, which is then factorized by the congruence generated by the axioms (in the categorical jargon, the result would be called the classifying HD of the theory). The "classifying" CA can be also generated in this way but not freely because expressing finiteness of the arities needs additional conditions that cannot be captures equationally (it is a well-known fact that the class of locally finite CA of an infinite dimension is not a variety, it is not a quasi-variety too). If we consider signatures in which all symbols have the same countable arity \omega, then the corresponding CA is freely generated by \Sigma (and then factorized by the theory congruence). The main advantage of HDs over locally finite CAs is that the finiteness of the arities is captured equationally (the trade-off is that HDs are algebras over graphs while CAs are algebras over sets). Note that the dimension/set of variables is a parameter in the above. An essentially different way of algebraizing logic is when variables are generators while the signature is a parameter. Semantically it means that a model is an evaluation of variables, another evaluation, even in the same carrier set, is another model. This is how validity of implications is defined. Theories in such logic are congruences (in contrast to Birkhoff's fully invariant congruences, when we talk about the equational logic), and we may call this way of algebraizing logic "congruental" (the term introduced by Blok and Pigozzi in their seminal work on algebraic logic). If Sign denotes a category of signatures and Log is a category of logics algebraically defined in a suitable way, then the HDs/CAs' way of algebraizing logic can be presented as a binary functor Sign x Set^op --> Log (signature elements are generators, the set of variables is a parameter). In congruental logic, we have a dual situation described by a functor Set x Sign^op --> Log (variables are generators, the signature is a parameter). Details can be found in my paper http://www.cs.toronto.edu/~zdiskin/Pubs/WAAL-97.pdf full of conjectures (deep insights are also possible :-). Zinovy On 5/28/07, Bill Lawvere wrote: > > > Hyperdoctrines (in many variants) were introduced as an algebraic > aspect of "proof theory" and as such are definitely not equivalent > to cylindric algebras (or polyadic algebras or even various categorical > formulations of logic). They involve fibered categories whose fibers > are cartesian closed (and with adjoints between the fibers etc.). > The poset reflection of these fibers are Heyting algebras. This > reflection process was intuited already by Curry and was later called > "the Curry-Howard isomorphism" even though this is a serious misnomer > because it is very far from being an isomorphism. > > (See my paper Adjoints in and among bi-categories, Logic & Algebra, > Lecture Notes in Pure and Applied Mathematics. 180:181-189. > Ed. A. Ursini, P Agliano, Marcel Dekker, Inc. Basel, 1996, > as well as the author's commentary on my paper Adjointness in > Foundations, as reprinted in TAC. > Recent papers of Matias Menni further clarify these developments, > which were partly inspired by work of Hans Laeuchli.) > > Conceptually, the problem of presentation of a theory in algebraic > logic by means of primitive predicates and axioms can be viewed as > taking place in two steps: first the presentation of a hyperdoctrine > with non-trivial fibers, and then the further collapse by imposing > the condition that projection maps act as inverse to diagonal maps > (within each fiber). This process can be localized. The problematic > existential quantifier which is the core problem of proof theory: > ("there exists a proof of ....") is thus split into several parts > to be studied separately. > > I hope the above helps to clarify the relationship between two > levels of categorical algebra. > > Bill > > > ************************************************************ > F. William Lawvere, Professor emeritus > Mathematics Department, State University of New York > 244 Mathematics Building, Buffalo, N.Y. 14260-2900 USA > Tel. 716-645-6284 > HOMEPAGE: http://www.acsu.buffalo.edu/~wlawvere > ************************************************************ From rrosebru@mta.ca Thu May 31 07:48:21 2007 -0300 Status: X-Status: X-Keywords: Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 31 May 2007 07:48:21 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1Hti3G-0000In-D7 for categories-list@mta.ca; Thu, 31 May 2007 07:38:42 -0300 Mime-Version: 1.0 Message-Id: Date: Thu, 31 May 2007 09:16:42 +0200 To: categories@mta.ca From: Anders Kock Subject: categories: preprint available Content-Type: text/plain; charset="us-ascii" ; format="flowed" Sender: cat-dist@mta.ca Precedence: bulk Dear all, This is to announce the availability of a preprint "Infinitesimal cubical structure, and higher connections" The preprint can be downloaded from http://arxiv.org/abs/0705.4406 or from my home page http://home.imf.au.dk/kock/ In the context of Synthetic Differential Geometry, we describe a notion of higher connection with values in a cubical groupoid. We do this by exploiting a certain structure of cubical complex derived from the first neighbourhood of the diagonal of a manifold. This cubical complex consists of infinitesimal parallelepipeda. Yours Anders From rrosebru@mta.ca Sun Jun 3 21:50:19 2007 -0300 Status: X-Status: X-Keywords: Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 03 Jun 2007 21:50:19 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1Hv0ab-0000ij-Mb for categories-list@mta.ca; Sun, 03 Jun 2007 21:38:29 -0300 From: Thomas Streicher Subject: categories: Re: hyperdoctrines and cylindric algebras To: categories@mta.ca Date: Thu, 31 May 2007 17:23:36 +0200 (CEST) MIME-Version: 1.0 Content-Transfer-Encoding: 7bit Content-Type: text/plain; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Couldn't one say that cylindric (and polyadic) algebras are awkward (from a categorical point of view) formulations of posetal hyperdoctrines over FinSet^op whose fibres are boolean algebras. So the pet objects of the algebraic logicians are certain *presentations* of particular hyperdoctrines. All this was worked out in a couple of papers by A. Daigneault beginning of 70ies. There is a lot of work by the algebraic logicians which I am not too familiar with. There arises the question whether their work is of any use for questions naturally arising to the categorical logician. That's how I understood Alex' question and what I'd like to know myself. Halmos was one of the first working on algebraic logic in the 50ies (polyadic algebras) and was later positive w.r.t. categorical logic. That's what I have heard of. Did he consider categorical logic as the "right formulation" of his original aims? Maybe senior categorists do know about this? Thomas